Entanglement phase diagrams from partial transpose moments

We present experimentally and numerically accessible quantities that can be used to differentiate among various families of random entangled states. To this end, we analyze the entanglement properties of bipartite reduced states of a tripartite pure state. We introduce a ratio of simple polynomials of low-order moments of the partially transposed reduced density matrix, and we show that this ratio takes well-defined values in the thermodynamic limit for various families of entangled states. This allows us to sharply distinguish entanglement phases in a way that can be understood from a quantum information perspective based on the spectrum of the partially transposed density matrix. We analyze in particular the entanglement phase diagram of Haar-random states, states resulting from the evolution of chaotic Hamiltonians, stabilizer states (which are outputs of Clifford circuits), matrix-product states, and fermionic Gaussian states. We show that for Haar-random states, the resulting phase diagram resembles the one obtained via the negativity, and that for all the cases mentioned above, a very distinctive behavior is observed. Our results can be used to experimentally test necessary conditions for different types of mixed-state randomness in quantum states formed in quantum computers and programmable quantum simulators.